Opposition parties say they will urge national assembly speaker Baleka Mbete to conduct the motion of no confidence vote in President Jacob Zuma by secret ballot.
The Economic Freedom Fighters (EFF) wrote to Mbete last week demanding the motion be held by secret ballot, accusing her of failing to "comprehend the important and urgent matter of the removal of [Zuma] from the office of presidency".
The party argued that an open vote would leave members of Parliament vulnerable to intimidation.
United Democratic Movement (UDM) leader Bantu Holomisa said his party supports the EFF's call for a secret ballot.
"We feel that notwithstanding the atmosphere outside that Zuma must go, people are still fearing him. This secret ballot will help them vote with their conscience. This includes those in the executive who are publicly defending Zuma not because they support him, but because they fear for their jobs," Holomisa said.
"This motion should have been held in Parliament latest by tomorrow, because we want Zuma removed before the [state of the nation address]. But because of the ANC's pride, they don't want to be seen to be taking instructions from opposition parties."
The no-confidence debate is scheduled for February 22.
Democratic Alliance (DA) chief whip John Steenshuisen said the party's leaders are meeting later this week and the motion will be discussed then, but it is "likely" that the DA will also push for a secret ballot.
"The sooner we get rid of Zuma, the sooner we can restore integrity in Parliament. A secret ballot allows for ANC members to vote without being victimised," he said.